WolframAlpha gives an answer in terms of an elliptic integral:

http://www.wolframalpha.com/input/?i=integrate(sqrt(sin(x)),%20x)

So I imagine that if we added those that we would be able to compute this.

Aaron Meurer

On Fri, Jul 6, 2012 at 10:00 AM, pallab <[email protected]> wrote:
>
>
> It seems sympy can not integrate sqrt(sin(x)).
>
> I did the following:
>
> import sympy as sm
> from sympy.abc import x,y,z
>
> tointegrate=sm.sqrt(sm.sin(y))
> sm.integrate(tointegrate)
>
> output is : Integral(sqrt(sin(y)), y)
>
> After a simple change of variable the integral is doable:
>
> def ytoz(z):
>     return(sm.asin(z))
>
> def dydz(z):
>     return(sm.diff(ytoz(z),z))
>
> subdict={y:cvytoz(z)}
> sm.integrate(dydz(z)*tointegrate.subs(subdict))
>
> output is : z**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,),
> z**2*exp_polar(2*I*pi))/(2*gamma(7/4))
>
> best,
>
> Pallab
>
>
>
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